Mathematics and Art: Mathematical Visualization in Art and Education

Front Cover
Claude Bruter
Springer Science & Business Media, Aug 21, 2002 - Mathematics - 337 pages
Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology.
For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.
 

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Contents

Presentation of the Colloquium The ARPAM Project
1
SolidSegment Sculptures
14
Visualizing Mathematics Online
25
The Design of 2Colour Wallpaper Patterns Using Methods Based on Chaotic Dynamics and Symmetry
39
Machines for Building Symmetry
57
The Mathematics of Tuning Musical Instruments a Simple Toolkit for Experiments
75
The Garden of Eden
85
Visualization and Dynamical Systems
87
Presentation of the Atractor
156
Forum Discussion
162
Forum Discussion
164
Getting Out of the Box and Into the Sphere
169
Constructing Wire Models
175
from Smale through The Optiverse
197
Tactile Mathematics
209
Hyperseeing Knots and Minimal Surfaces
219

Mathematical Aspects in the Second Viennese School of Music
101
The Film Series
115
Guided Tours of Buried Galleries Inside a Computer
131
A Mathematical Interpretation of Expressive Intonation
137
Symbolic Sculptures
145
How Art Can Help the Teaching of Mathematics?
149
Forum Discussion
151
Ruled Sculptures
229
A Gallery of Algebraic Surfaces
233
The Mathematical Exploratorium
263
Copper Engravings
269
Color Plates
271
Index
331
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